SIZE-SELECTIVE SEX-ALLOCATION AND HOST FEEDING IN A PARASITOID HOST MODEL

1. Hymenopterous parasitoids frequently exhibit (a) size-selective sex-allocation, laying predominantly male eggs in smaller host individuals and female eggs in larger hosts, and (b) size-selective host-feeding, i.e. feeding on and killing, but not parasitizing, smaller host individuals. We abbreviate size-selective sex-allocation and host-feeding by SSH. We analyse a parasitoid-host model incorporating SSH that recognizes the following: overlapping generations, an invulnerable adult host stage, a young immature stage, an old immature host stage, and only the female parasitoid. We assume that young immature hosts are attacked by the parasitoids, die as a consequence, but do not contribute to the juvenile female parasitoid population; each attack on an old immature host produces a juvenile female parasitoid. 2. SSH leads to delayed pseudo-density-dependence in recruitment to the parasitoid population because the current attack rate on young immatures, which is a function of parasitoid density, influences the future number of old immatures and hence the future per head rate of recruitment of searching parasitoids. SSH has two effects on the model's stability properties. (a) It is potentially stabilizing because it tends to suppress the inherent long-period host-parasitoid cycles. This stabilizing propensity is enhanced when the adult host stage lasts about as long as or longer than the entire immature stage, the immature parasitoid stage is short-lived, and the young immature host stage is not too long-lived or the attack rate on it is not too high. (b) SSH can also destabilize the model by creating a region of instability in which cycles occur with a period related to the total length of the host immature stages. These shorter-period cycles are promoted by the same features that tend to suppress the underlying parasitoid-host cycles. 3. Small perturbations from equilibrium in the locally stable region of parameter space are followed by damped oscillations. However, because of the presence of a multiple attractor, in much of the locally stable region large perturbations may be followed by limit cycles, commonly of the type seen in the new unstable region.